When you put a stake in the ground it can be just to put up a tent, or to use a stake to tether an animal to. (Obviously we are talking about a stake is a sharpened piece of wood that can be driven into the ground, and not one of the other meanings.) But I imagine the context of Mr. Thompson's query has to do with claiming the ground as part of a claim of the land to be used as a home, or a new building, or a mining site.

The phrase "pulling up stakes," meaning to move, has an antonym, putting down stakes or setting stakes, meaning to pitch one's tent or to settle down. The OED has a number of examples of the former, and a few of the latter, e.g.,

1872 SCHELE DE VERE Americanisms 184 Where he settles, there he stakes or sticks his stakes. 1906 Outing (U.S.) Feb. 605/2 After drifting about several years I finally drove stakes on the Spokane River. . . .1949 Boston Globe 15 May (Fiction Mag.) 6/2 We'll set our stakes, an' I'll slip down to Dawson an' record the claim.

The U.S. has had many occasions for people to claim for themselves unclaimed land, in various land rushes in the settling of territory considered unsettled (because the aboriginal natives didn't use fences or claim the land as private property). So new settlers would set stakes to claim land in one of these rushes.

They would also claim a site, or stake a claim, for themselves during a Gold Rush (like that of 1849) by marking the ground with stakes.

I think Mr. Thompson's source is saying that this is where he will pitch his tent, perhaps to live, or perhaps to say, metaphorically, "This is my stand." I haven't seen the context, and wouldn't know how to choose among the alternatives. SS